Question

Factorize each of the following algebraic expression:
49 − x² − y² + 2xy

Answer 1

$$\begin{gathered} 49-{\mathrm{x}}^2-{\mathrm{y}}^2+2\mathrm{xy} \\ =49-({\mathrm{x}}^2-2\mathrm{xy}+{\mathrm{y}}^2) \\ =49-({\mathrm{x}}^2-2\times \mathrm{x}\times \mathrm{y}+{\mathrm{y}}^2) \\ =7^2-(\mathrm{x}-\mathrm{y}{)}^2 \\ =[7-(\mathrm{x}-\mathrm{y})\left]\right[7+(\mathrm{x}-\mathrm{y})] \\ =(7-\mathrm{x}+\mathrm{y}\left)\right(7+\mathrm{x}-\mathrm{y}) \\ =(\mathrm{x}-\mathrm{y}+7\left)\right(\mathrm{y}-\mathrm{x}+7) \end{gathered}$$